Conservation Laws and Symmetry Properties of Scalar-Tensor Gravitational Theories

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Abstract
Scalar-tensor (ST) analogs of the Einstein pseudotensor, the von Freud superpotential, the Møller superpotential, and the Komar vector are derived and used to form conservation laws appropriate to any version of the ST gravitational theory. When applied to a ST central-mass field, the conservation laws are found to yield correct values for total energy and momentum. The scalar field is shown to affect, in general, not only the form of the conservation laws but, through its symmetry properties, the identification of physically significant conserved quantities. It is pointed out that ST-conserved complexes have units of energy and momentum only in certain versions of the theory (e.g., the Brans-Dicke version).